Simplify the following expression: $y = \dfrac{-9q^2 + 126q - 360}{q - 10} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ y =\dfrac{-9(q^2 - 14q + 40)}{q - 10} $ Then we factor the remaining polynomial: $q^2 {-14}q + {40} $ ${-10} {-4} = {-14}$ ${-10} \times {-4} = {40}$ $ (q {-10}) (q {-4}) $ This gives us a factored expression: $\dfrac{-9(q {-10}) (q {-4})}{q - 10}$ We can divide the numerator and denominator by $(q + 10)$ on condition that $q \neq 10$ Therefore $y = -9(q - 4); q \neq 10$